ERIC ED592477: Variations on a Theme: Pre-Service Mathematics Teacher Reflections Using an Affect-Based Critical Moment Protocol

2018·0.47 MB·English

by  ERIC

Marshman, Galligan, Axelsen, Woolcott, & Whannell
Variations on a Theme: Pre-service Mathematics Teacher
Reflections Using an Affect-based Critical Moment Protocol
Margaret Marshman Linda Galligan
University of the Sunshine Coast University of Southern Queensland
<[email protected]> <[email protected]>

Taryn Axelsen Geoff Woolcott
University of Southern Queensland Southern Cross University
<[email protected]> <[email protected]>

Robert Whannell
University of New England
<[email protected]>

Examining critical incidents in the mathematics classroom is a useful way for pre-service
teachers to understand the experience of teaching. This paper examines the development and
trialling of variations of a novel affect-based critical moment protocol that enables pre-
service mathematics teachers to reflect on their teaching performance. The emotions
experienced in these moments were examined using self and group reflection, considering
the thoughts and actions occurring immediately prior to, or during those moments. The four
case studies presented report on trialled variations of this reflection process in a range of
programs and delivery modes in four regional Australian universities.
Teacher performance is generally assessed by observation of classroom practice. In
initial teacher education (ITE) programs, such observations are traditionally made by a
mentor classroom teacher during practicum. There is a multitude of processes and literature
around the practicum experience and an expansion in the range of strategies designed to
improve teaching performance, including group or team reflection strategies (Woolcott et
al., 2017). Studies of critical incidents (events) and/or critical moments, which include
reflective pedagogical analysis and interpretation, provide an important way of determining
the aspects of a lesson to examine and improve teaching performance (Tripp, 2011; Yeigh
et al., 2016).
Critical incidents and critical moments, often treated or identified separately, have
become important, in developing the reflective practices of teachers and in ITE (Griffin,
2003). Studies focussing on critical moments have included emotion and/or affect of pre-
service teachers (PSTs) (Yeigh et al., 2016), and detailed measures of teachers’ emotional
states at particular times in a classroom (Tobin & Richie, 2012), but both critical incidents
and critical moments are largely determined through observation of teaching as it is related
to student learning. The lack of reliability and validity of findings from observational studies
is widely reported (Madigan & Ryan, 2011) and critical incident or critical moment protocols
do not escape this uncertainty. They are necessarily judgmental and, in pre-service practicum
their effectiveness may be constrained by subjective differences in evaluations of both
competence and confidence by an observer (Huntly, 2011).
Practicum can be an emotional experience and the emotional content of critical incidents
or moments requires careful consideration. The critical moment protocol discussed in this
article deals with self-determined emotion or affect as an important discussion point for
2018. In Hunter, J., Perger, P., & Darragh, L. (Eds.). Making waves, opening spaces (Proceedings of
the 41st annual conference of the Mathematics Education Research Group of Australasia) pp. 511-
518. Auckland: MERGA.
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reflective self-evaluation of teaching performance. The innovative protocol presented here
was developed in a project investigating how to increase the perceived teaching competence
and confidence of mathematics and science PSTs. The protocol builds on teaching
performance being linked to how an individual feels at particular moments during teaching
(Ritchie et al., 2014). The protocol includes affect-based critical moment analysis as part of
the PST learning experience, sometimes, but not always, referring back to incidents or
thinking processes immediately prior.
Background
Critical incident analysis in the classroom began in the late 1980s, and was used as a
focus for reflective practice, for example in the case of a behavioural incident (e.g., spitting
in class, see Tripp, 2011). Meyer and Land (2005) extended the conceptualisation of critical
incidents to include those when threshold concepts are understood, that is, when previously
inaccessible ideas are understood which lead to “significant shifts in perception of a subject”
(p. 373). This concept extension embraces ‘teachable moments’, when either a
misconception has been observed or a desire to know has been sparked in the students
providing a teaching opportunity (Patahuddin & Lowrie, 2015) to develop deeper conceptual
understanding (Griffin & Ward, 2015). Woods (2012) proposed that, as a critical incident is
unplanned and unanticipated there is a higher potential for impact on the affective/emotional
state. Recent developments have broadened the conceptualisation as critical moments are
not distinguished primarily on the basis of an event or incident and can be used to exam
learning in a range of different contexts (Woolcott et al., 2017). In ITE, for example, PSTs
can use critical moment analysis to improve their classroom performance while on
practicum.
This report uses the term ‘affect-based critical moments’ to distinguish lesson
performance foci from the event-based critical incidents discussed above. The protocol was
developed as a part of a broader project, It’s part of my life: Engaging university and
community to enhance science and mathematics education (IPOML), undertaken across the
Regional Universities Network (RUN) (Woolcott et al., 2017). The project developed around
a model derived from teacher education processes related to a collaboration nexus,
previously described for Australian contexts (Gahan et al., 2011). The Enhancement-Lesson-
Reflection (ELR) process (Figure 1a) was designed and trialled to develop the perceived
competence and confidence of PSTs to engage with and inspire classroom science and
mathematics learners. The ELR process shows PSTs how to use science and mathematics to
solve problems in their local region through collaborations with university and community
experts. Ideally, the ELR process is iterated (Figure 1b) and 1, 2, 3 and 5 cycle iterations
have been documented.
Initially the critical moment protocol was used in face-to-face reflection sessions, but
this article aims to examine trialled variations of this reflection process adapted to a range
of programs and delivery modes across the RUN universities. This protocol is supported in
most cases by peer observers and university educators through engagement in collaborative
group reflection following self-reflection on selected positive and negative critical moments.
The reflection has an added dimension in being structured around lesson study.
The critical moment protocol
Each teaching PST was asked to identify, from the video of their lesson, a number of
critical moments, representing an important (positive or negative) emotional feeling or
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experience. In initial trials, PSTs identified two critical moments, generally less than two
minutes in duration, for each third of the lesson and recorded their perception of the start and
end time for each moment. Later trials used variations adapted to their teaching contexts
depending on whether PSTs were: attending a face-to-face session at a university campus
with university educators and mathematicians; teaching classroom students, large school
groups at a university campus or peers in a university class; and/or, undertaking a group
reflection either face-to-face or online (Table 1). An emotion diary (Ritchie et al., 2014,
Yeigh et al., 2016), such as seen in Figure 1c, was used by both the teaching and observing
PSTs to explore experienced or observed emotions from the lesson. An individual may feel
different emotions at different times while teaching mathematics/science and this protocol
allows PSTs to consider and reflect on the emotions they associated with each critical
moment.

Emotion Plheaaspep edneisncgri bane db raite wflyh owmha tth yeo eum woetrioen d woiansg d, wirehcatte wd.a s
Excitement/Enthusiasm

Happiness
Enjoyment

Pride
Anxiety/Worry
Frustration
Disgust/Contempt
Annoyed/Irritated
Disappointment
Embarrassed
Interested
Confident

Figure 1.a. The Enhancement-Lesson-Reflection (ELR) process. b. The iterative path of the ELR process. c.
The initial emotion diary with emotions; Excitement/Enthusiasm, Happiness, Enjoyment, Pride,
Anxiety/Worry, Frustration, Disgust/Contempt, Annoyed/Irritated, Disappointed, Embarrassment, Interested
and Confident
The teaching PST then engaged in a reflection, ideally as a group discussion guided by
university educators, concerning what the teaching PST was doing or thinking just prior to
and during each critical moment. The reflection discussion is structured around the following
questions:
1. What happened that made you see this as a critical moment? What were you doing or
thinking just before this moment?
2. What was the main emotion you felt at the time? How strongly was it felt?
3. (If reflecting with others) What did others think about your emotion? Was it the same
as your view?
4. What would you do if you had an opportunity to recreate that moment in future
lessons?
This served to focus how a PST could utilise or maintain positive, or perhaps change
negative, emotions during future lessons. This paper examines the critical moments being
selected by the PSTs and their reflections to determine: How engaging with variations of the
critical moment protocol can facilitate change in PSTs’ confidence and competence when
teaching mathematics; and, How protocol variations can be successfully adapted to a range
of ITE contexts.
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The Study
A mixed methods approach involving four embedded case studies is reported. Cases
were purposefully selected based on their focus on mathematics teaching, but present a
diversity of characteristics with respect to mode of delivery, program variation (including
number of iterations of the process), geographic distribution, size of PST and school student
cohorts involved, and availability of mathematics experts. The variation between cases
provided an opportunity to compare the effect of the protocol and better understand its
deployment across this diversity and the associated variation in protocol implementation.
The case studies and participants are summarised in Table 1.
Table 1
Reflection process variations reported in this study in Cases 1 through 4
Trial delivery context Reflection Reflection process
participants variation
Case 1: Reflection on campus, on Four PSTs from a Self and group reflection
lessons delivered at a school (Year BEd-Primary and face-to-face with
6) three university university educators,
educators ELR with 3 iterations
Case 2: Reflection on campus A class (40 students) Class reflection face-to-
within university tutorials, on of one-year Grad Dip face with university
presentation of conference posters of Education educator, assignment
by two PSTS (Primary) and one submission including a
university educator written self-reflection,
ELR with 2 iterations
Case 3: Reflection during a series Five secondary PSTs Face-to-face reflection
of community events every 3 weeks and up to six with PSTs outside of
at a university campus (25-40 Year university educators event at university
9 and 10 students from 15 schools), campus, ELR with 5
PST delivered lesson face-to-face iterations
and online as part of ELR
Case 4: ELR online (asynchronous A class of PSTs Self-reflection
and synchronous), instruction (secondary assignment supported by
embedded into the university mathematics) and one a video of the lesson and
Learning Management System for university educator PST recollection of
an assessment task built around the experiences during
reflection teaching, 1 iteration
Data collection and participants
Data from the four separate cases outlined in Table 1 were collected from June 2013 to
December 2016. In each case the entire ELR process involved either a group of up to six
PSTs or a larger tutorial group, up to three university educators, and/or up to two university
mathematicians, who collaborated to help develop mathematics lessons, poster presentations
or workshops delivered by the PSTs. In Case 4, PSTs worked in partnership with community
mathematics experts. Reflections were assisted by the educators, either in face-to-face,
blended or online (synchronous and asynchronous) learning environments, and/or assessed
as an assignment within the university education curriculum.
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Data collected included video transcripts of the reflection sessions, as well as transcribed
or written responses of participants in semi-structured interviews, recorded after each lesson,
as well as prior to or after a reflection session. The semi-structured interviews allowed for
flexible exploration of emerging themes as interviews unfolded. Data were also available in
the written responses made on forms included in the protocol resourcing.
Data analysis
Data were first coded and scored using constant comparative analysis and then coded to
nodes using the qualitative data analysis software NVivo Version 10 (QSR International).
The nodes were then cross-coded with categories of meaning significant to emergent themes.
The researchers responsible for implementation in each case provided an overall summary
of each case that was also used to identify key themes, identify process changes over time
and to clarify similarities and differences in implementation.
Results and discussion
This section discusses how, for each case study, PST confidence and perceived
competence was supported using the affective based critical moment protocol.
The effect of common protocol components
All PSTs reported increased confidence and competence following collaboration and/or
self-reflection—no negative feedback was reported. Interestingly, PSTs reported increased
confidence when others did not notice their negative emotional states, since this meant that
any lack of confidence felt by them was not noticed by observers (and, therefore, not
something the PST should worry about). One PST went further in noting:
… the fact that our peers don’t really notice when a student teacher has a negative critical moment
can be flipped. I have been able to spot that ‘glazed’ look on students’ faces when they don’t
understand a concept being taught, which is particularly useful when they do not vocalise their lack
of understanding. (PST)
Another typical comment, supported by Tripp (2011), was that no one had previously
asked the PSTs how they felt during their teaching, even though it was a very emotional
time. This comment echoes the stress of the practicum experience, a stress that perhaps
observing teachers and university educators do not always acknowledge:
The opportunity to have a peer observation and reflection program in a real classroom setting allowed
us to allay our fears and stresses with our peers and university educators as observing mentors. That
our feelings were acknowledged helped to build our confidence. On prac, the mentor never actually
asked ‘How do you feel?’ (PST)
The protocol allowed PSTs to play a stronger role than when observer reports are used
for reflection, as PSTs facilitate their own self-judgement and self-determination. The focus
on short self-identified elements was the subject of a comment in Case 2—the PST identified
a negative moment as after students misunderstood a teaching instruction, or positive
moment as when students presenting in classroom feedback were able to demonstrate to the
class an understanding of the intent of the curriculum point:
The reflection process provides a very effective structure that encourages reflecting carefully on
smaller sections of their lesson rather than retelling the whole experience which can often not lead to
significant improvements. By looking at small sections of the lesson, this method is non-threatening
and appears to lead to much more specific discussion and then improvements. (Educator)
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The commonality of process was evident in comments from the workshops in Case 3,
where PSTs conducted mathematical modelling enrichment classes (Axelsen et al., 2017)
with school students, but with separate enhancement and reflection sessions. An emerging
theme was the support that such a collaborative reflection provided—support lacking in
practicum contexts, but common to all variations reported here:
Compared to going on pracs, in this program there is much more of a review process and you can
have that enhancement and for me that was really important. For me it confronted me and made me
change my teaching track and that was because I had the opportunity to sit back and look at how I
had gone. Because in prac there is none of that; there is no review—it is more about ticking the boxes.
(PST)
While reflection variations that included iterations provided feedback mechanisms that
led to improved confidence and competence, PSTs using the single iteration seen in the
assignment of Case 4 appear to have gained some benefit also:
The reflection process has shown me just how much I can learn from videoing myself teaching a
lesson, watching it and reflecting on it. Whilst I was aware of the benefits of reflection as determined
by lecturers and texts, I had not yet actively engaged in ‘watching myself teach’. This process allowed
me to critically reflect upon everything from my body language to the way I explained difficult
concepts and thus learn how to better myself as a teacher. In the future, I will aim to consistently
reflect upon my teaching, videoing lessons and gaining feedback from students when possible, so that
I can continue to learn from my mistakes and recreate my successes. (PST)
PSTs believed the protocol assisted them develop their ongoing mathematics teaching:
In terms of lesson plan reflections, it is easy to see that although other pre-service students may have
not noticed anything wrong, in some cases a mentor will have noticed such things. Importantly, the
ability to take constructive criticism is easier when a student teacher already has an idea of what might
have not been working. This is a kind of preparedness for critical feedback. Again on my 2nd
practicum, where I at least feel a lot more is expected of me and my mentor has certainly expected a
lot, the experience of emotion diaries (the video reflection as a whole) has allowed me to cope better
with this experience. (PST)
Most importantly, the protocol enabled PSTs to also consider emotion, including those
of their students, as an indicator of teaching effectiveness. For example, in response to the
question, “What aspects of the trial did you find most interesting?” posed after a lesson, one
PST said:
Reflecting on emotions rather than practice, assessing student emotions instead of performance based
assessment, assessing key emotional moments that others are possibly unaware of (PST)
The effect of protocol variations
The ELR protocol as initially trialled in Case 1 (Figures 1a and 1b) became ‘variations
on a theme’, as the ELR process and the critical moment reflection protocol, was adapted in
other ITE programs. Case 1 may be seen as an ideal way to improve confidence and
competence in PSTs in practicum, although it would be time and resource consuming unless
it was adapted more directly to on-site utilisation with enhancement and reflection sitting
alongside lesson delivery (see Woolcott et al., 2017).
In Case 2, the effect was similar, but in an adaptation to a university tutorial class, rather
than a school class. The enhancement occurred with mathematicians in lectures and the
educator modelled the critical emotion reflection process using two critical moments from a
previous lecture—one positive, one negative—and invited the pre-service teachers to reflect
on them with her. After poster presentations, two PSTs taught lessons to their peers based
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on their posters. PSTs then identified critical moments from the video recording, followed
by a group rating of these critical moments and group reflection and discussion.
The experience changed their way of thinking. It opened their eyes that maths isn’t so prescriptive.
They complained that the emphasis was on thinking—so it pushed them. It changed their mindset.
(Educator)
Case 3 illustrates the ELR reflection protocol in a workshop context, a context that may
easily be adapted to professional learning experiences (Woolcott et al., 2017). The educator
facilitated the reflection process where PSTs, an educator and mathematician reflected after
a workshop and then discussed the plan for the next workshop. The lesson and reflections
session was repeated every three weeks for five iterations. All PSTs taught a lesson. The
iterative process helped reduce PSTs’ nervousness with regard to teaching mathematical
modelling with its open-ended nature of inquiry:
I had been pretty nervous dealing with the unknowns but coming in today on the back of the other
sessions, it’s not going to be that difficult. (PST)
The Enhancement–Lesson–Reflection process taught me a lot about trying to get the kids more
engaged. It helped me to focus on the maths side of things rather than focusing (too much) on the
modelling process. It taught me to try to get the kids engaged without giving them too much. It taught
me to make it (the problem) real life with lots of variables and to facilitate rather than telling them
(the students) how to do it. It really taught me to change the way I teach. (PST)
In contrast, Case 4 successfully adapted the critical moment protocol to teaching PSTs
studying online. The reflection phase required self-reflection on three critical moments for
short lesson segments taught to peers (family and friends in most cases). The self-reflection
was completed as an assignment supported by viewing a video of the lesson. Students who
fully engaged in this task reported that it was demanding, but beneficial:
The final assessment task was very challenging, however provided an excellent opportunity for
reflection and skill development. (PST)
Conclusion
Findings from these variations support the use of the critical moment protocol in
examining the impact of emotions on thinking and behaviour in the PSTs’ classroom
teaching experience. PSTs learnt how to identify and analyse their teaching-related affective
states in order to assess their own emotions and to understand the relationship between
emotional literacy and effective pedagogy (Woolcott et al., 2017; Yeigh et al., 2016). Many
PSTs valued reflecting with a video of their lesson. The educator emphasised the importance
of using critical moments, small sections of the lesson, rather than the whole lesson, since
this led to more focussed discussions in the reflection sessions so that PSTs could identify
specific aspects for improving their teaching. PSTs also acknowledged that the collaborative
nature of the ELR sessions improved their confidence and competence.
The study emphasises the importance of reflective analysis of affect for teacher
performance, and thus links the affective protocol to increasing competence through
increased pedagogical confidence. The critical moment protocol appears to be a method that
can be embraced easily by PSTs, and potentially by teachers to support a reflective process
for improving teaching and learning, and which appears to be relatively non-judgmental,
being essentially a self-regulatory process.
Ensuring those who facilitate reflection and affective analysis are skilled in guiding PSTs
in the exploration of their experiences, while also considering the perspectives of peers and
pedagogical mentors, appears essential. Overall, these findings indicate that it is important
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for PSTs to better connect emotional awareness to their teaching goals, as an aspect of
pedagogical confidence and competence. These findings appear to be consistent across all
the variations of the protocol supporting its adaptability, although additional research and
trialling is needed to determine long-term effectiveness of the process.
Acknowledgements
This paper reports on research associated with the project, It’s part of my life: Engaging
university and community to enhance science and mathematics education, a project
supported by a three-year $1 million grant awarded to the Regional Universities Network by
the Australian Government Office for Learning and Teaching.
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